Abstract
This paper focuses on a new type of configuration design of a compliant parallel mechanism (CPM) planar continuum structure and its characteristic analysis of vibration-inherent frequency for planar motion, which can suppress the impact of random vibration in ultra-precision positioning and manufacturing equipment and improve the inherent frequency response of the mechanism. Firstly, a vector-mapping isomorphism between the fully CPM and conventional isomorphic parallel mechanism was constructed with a kinematic differential Jacobian matrix. Then, the mathematical model of topology optimization was put forward considering the compromise programming on the static stiffness and mean vibration-inherent frequency of the mechanism as the design variable and the minimization of compliance as the objective function. A constraint of volume fraction was considered and multi-objective micro displacement mechanism topology optimization based on a prismatic-revolute-revolute (3-PRR) planar nano-positioning continuum structure was performed using the solid isotropic material with penalization (SIMP) technique, which combines the criteria of the optimization algorithm and the vector isomorphic mapping method. Multi-objective topology optimization of the continuum structure micro displacement mechanism was investigated and presented by optimizations with different initial rejection rates. The simulation results show that the stiffness and vibration suppression performance of the continuum structure were improved, whereas the positioning of differential kinematics characteristics of the 3-PRR micro displacement planar fully CPM and isomorphic prototype mechanism retain the same. The modal analysis also provides a rational configuration for the micro displacement mechanism dimensional design and its optimal modal parameters. The crossover oscillation in frequency response of the continuum structure was reduced and quickly converged in the optimization iterations. The performance of the optimized mechanism was verified by the experiments on a planar fully compliant micro displacement continuum structure based on Lead Zirconate Titanate (PZT) actuator.
Highlights
Nowadays, positioning mechanical components becomes very important for micro/nano applications such as cell manipulation, surgery, aerospace, micro fluidics, optical systems, micro machining and micro assembly etc. [1]
A continuum structure isomorphic mechanism design method using multi-objective topology optimization is proposed, which is based on differential movement vector isomorphic mapping with a 3-PRR planar fully compliant parallel mechanism (CPM) prototype
A homologous mechanism of 3-PRR in a holonomic material was constructed with vector isomorphic mapping
Summary
Nowadays, positioning mechanical components becomes very important for micro/nano applications such as cell manipulation, surgery, aerospace, micro fluidics, optical systems, micro machining and micro assembly etc. [1]. Parallel kinematic structures are mostly employed in micro positioning stages because of their advantages such as zero backlash, no need for lubrication, reduced wear, high precision, compact structure and monolithic configuration, but puzzled by their limited workspace, dexterity, non-linear kinematics, and difficult calculation of forward kinematics [3] These drawbacks can be avoided for flexure-based compliant mechanisms because of their micro range motion. Various types of CPMs have been used in compliant positioning stages in the literature These mechanisms are based on rigid body parallel prototypes. The method neither directly reflects the kinematics and dynamics performance nor effectively meets high-precision positioning requirements It can be processed with all the flexible hinges being integrated into a continuum structure using WEDM (Wire-cut Electrical Discharge Machining). FiFgiugurere1.1.SStrtruuccttuurreeooff33--PPRRRR ppllaannaarr ppaarraalllelellpprorotototytyppe emmanainpiupluatloarto, (ra, )(aa)ctaicvteivpeaiprasiirnsteinrsteecrtseedctwedithwith eaecahchooththeer;r;(b(b))aaccttiivveeppaaiirrss iinntteerrsseecctteeddaattaappooinint.t
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